Concept-wise Practice

reciprocal-sum MCQ Questions for Class 10

reciprocal-sum se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.

Practice Questions

2 questions tagged with reciprocal-sum.

Question 1/2 Hard Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 27

यदि \(\alpha=2+\sqrt{5}\) और \(\beta=2-\sqrt{5}\), तो \(\frac{1}{\alpha}+\frac{1}{\beta}\) क्या है?

If \(\alpha=2+\sqrt{5}\) and \(\beta=2-\sqrt{5}\), what is \(\frac{1}{\alpha}+\frac{1}{\beta}\)?

Explanation opens after your attempt
Correct Answer

A. (-4)

Step 1

Concept

\(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}=\frac{4}{4-5}=-4\). Finding sum and product first is easier.

Step 2

Why this answer is correct

The correct answer is A. (-4). \(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}=\frac{4}{4-5}=-4\). Finding sum and product first is easier.

Step 3

Exam Tip

\(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}=\frac{4}{4-5}=-4\)। पहले योग और गुणनफल निकालना आसान रहता है।

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Question 2/2 Hard Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 26

यदि \(\alpha=5+\sqrt{6}\) और \(\beta=5-\sqrt{6}\), तो \(\frac{1}{\alpha}+\frac{1}{\beta}\) क्या है?

If \(\alpha=5+\sqrt{6}\) and \(\beta=5-\sqrt{6}\), what is \(\frac{1}{\alpha}+\frac{1}{\beta}\)?

Explanation opens after your attempt
Correct Answer

A. \(\frac{10}{19}\)

Step 1

Concept

\(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}\). Here the sum is (10) and product is (25-6=19), so the answer is \(\frac{10}{19}\).

Step 2

Why this answer is correct

The correct answer is A. \(\frac{10}{19}\). \(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}\). Here the sum is (10) and product is (25-6=19), so the answer is \(\frac{10}{19}\).

Step 3

Exam Tip

\(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}\) होता है। यहाँ योग (10) और गुणनफल (25-6=19), इसलिए उत्तर \(\frac{10}{19}\) है।

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